This simple regression analysis examines the relationship between MBA GPA (dependent variable) and GMAT scores (independent variable) for 202 students. The regression equation shows that MBA GPA increases by 0.00311 for every point increase in GMAT score, explaining 45.6% of the variation in GPA. A multiple regression adds undergraduate GPA and age as additional predictors, finding GMAT and UGPA to be significant predictors of MBA GPA while age is not a significant predictor.

1. 1
Regression Analysis Project
Professor Sangit Chatterjee
Rudy Parker
Parker.ru@neu.edu

2. 2
Simple Regression analysis MBA GPA Versus GMAT
RegressionAnalysis: MBA GPA versus GMAT
The regression equation is
MBA GPA = 1.39 + 0.00311 GMAT
Predictor Coef SE Coef T P
Constant 1.3923 0.1387 10.04 0.000
GMAT 0.0031142 0.0002403 12.96 0.000
S = 0.236514 R-Sq = 45.6% R-Sq(adj) = 45.4%
PRESS = 11.4007 R-Sq(pred) = 44.60%
Analysis of Variance
Source DF SS MS F P
Regression 1 9.3921 9.3921 167.90 0.000
Residual Error 200 11.1877 0.0559
Total 201 20.5798
5 rows with no replicates
Unusual Observations
Obs GMAT MBA GPA Fit SE Fit Residual St Resid
3 510 3.7450 2.9805 0.0225 0.7645 3.25R
21 540 3.5460 3.0739 0.0184 0.4721 2.00R
39 680 2.9430 3.5099 0.0306 -0.5669 -2.42R
49 570 2.6080 3.1674 0.0167 -0.5594 -2.37R
63 750 3.8180 3.7279 0.0457 0.0901 0.39 X

3. 3
74 500 3.5680 2.9494 0.0242 0.6186 2.63R
95 520 3.5170 3.0117 0.0210 0.5053 2.15R
106 740 3.5200 3.6968 0.0435 -0.1768 -0.76 X
107 570 2.5090 3.1674 0.0167 -0.6584 -2.79R
127 670 3.9520 3.4788 0.0286 0.4732 2.02R
132 400 2.4680 2.6380 0.0448 -0.1700 -0.73 X
137 760 3.8800 3.7591 0.0479 0.1209 0.52 X
142 460 3.4660 2.8248 0.0318 0.6412 2.74R
149 590 2.7080 3.2297 0.0171 -0.5217 -2.21R
155 760 4.0000 3.7591 0.0479 0.2409 1.04 X
173 630 3.8940 3.3542 0.0216 0.5398 2.29R
176 560 3.6230 3.1362 0.0169 0.4868 2.06R
196 500 3.6400 2.9494 0.0242 0.6906 2.94R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
Durbin-Watson statistic = 1.92488
No evidence of lack of fit (P >= 0.1).
GMAT
MBAGPA
800700600500400
4.00
3.75
3.50
3.25
3.00
2.75
2.50
Scatterplot of MBA GPA vs GMAT

4. 4
This simple regression analysis is looking at the response of MBA GPA scores to the
explanatory variable GMAT.
The R-Squared statistic is 45.6%, which means that 45.6% of the MBA GPA score is
determined by the GMAT score. This is a reasonably strong positive correlation. It is a
reflection of the fact that SSR is 9.39 over SST of 20.79. This means the error is only
11.18.
There were 202 observations made. The GMAT scores of the MBA students varied from
400 to 760. The GPA scores varied from 2.4 to 4. The line in the figure is the least-
squares regression line for predicting GPA from GMAT. The equation of the line is
Predicted GPA = 1.39 + 0.00311 x GMAT
GPA rises by 0.00311 for every point rise in GMAT score.
Testing the confidence interval of 95% for the slope b of the regression line is
b +/- t* Seb
t* is the value for the t(n-2) density curve.
B = 0.0031142 +/- 1.97 * 0.0002403 (0.002640809, 0.003587591)
Testing the null hypothesis
H: B = 0
H: B does not equal 0
P= 0
Alpha = 0.05
Therefore P < alpha & we reject the null hypothesis.
My conclusion is that GPA can be predicted from GMAT Scores.
Residual Plots for MBAGPA
One-way ANOVA: MBAGPA versus GMAT

5. 5
Source DF SS MS F P
GMAT 31 11.2455 0.3628 6.61 0.000
Error 170 9.3343 0.0549
Total 201 20.5798
S = 0.2343 R-Sq = 54.64% R-Sq(adj) = 46.37%
Individual 95% CIs for MeanBasedon
Pooled StDev
Level N Mean StDev -------+---------+---------+---------+--
400 1 2.4680 * (-------*-------)
430 3 2.6843 0.1635 (----*---)
450 1 2.7360 * (-------*------)
460 6 2.8713 0.3118 (--*--)
470 6 2.8057 0.1378 (--*--)
480 5 3.0168 0.1978 (--*---)
490 4 2.8965 0.2281 (---*---)
500 7 3.0649 0.4108 (--*--)
510 9 3.0948 0.3097 (--*-)
520 11 3.0297 0.2477 (-*--)
530 4 3.0195 0.1642 (---*---)
540 15 3.0973 0.2043 (-*-)
550 6 3.3063 0.1712 (--*--)
560 12 3.0872 0.2708 (-*--)
570 21 3.0350 0.2312 (-*)
580 11 3.2226 0.1961 (--*-)
590 9 3.0913 0.2472 (--*-)
600 12 3.2447 0.1590 (-*-)
610 13 3.2093 0.2230 (-*--)
620 3 3.4277 0.1328 (---*----)
630 4 3.4870 0.3126 (---*---)
640 5 3.2792 0.1564 (---*--)
650 5 3.4414 0.1801 (--*---)
660 3 3.4580 0.1963 (----*---)
670 10 3.5587 0.2121 (-*--)
680 4 3.3727 0.3693 (---*---)
690 4 3.5960 0.1742 (---*---)
700 3 3.7873 0.0783 (---*----)
720 1 3.7200 * (-------*-------)
740 1 3.5200 * (-------*------)
750 1 3.8180 * (-------*------)
760 2 3.9400 0.0849 (-----*----)
-------+---------+---------+---------+--
2.40 3.00 3.60 4.20
Pooled StDev = 0.2343
It’s interesting to note that the confidence intervals for GMAT scores to MBA GPA seem
to be the largest at either ends of the GMAT spectrum. This seems to suggest that people
with very high or very low scores need to be looked at slightly differently from the usual.
Perhaps certain people are very bad at standardized tests and get nervous. In an MBA
program they could perform far higher than anticipated. Equally, there are some
individuals who are very good at quantitative analysis and tests, yet they cannot work in

6. 6
teams due to other factors such as lack of team-working abilities or low ‘EQ’. This would
thus bring their GPA down considerably below that anticipated.
Multiple Regression Analysis MBA GPA versus GMAT, UGPA, Age
RegressionAnalysis: MBA GPA versus GMAT, UGPA, Age
The regression equation is
MBA GPA = 0.871 + 0.00228 GMAT + 0.297 UGPA + 0.00543 Age
Predictor Coef SE Coef T P
Constant 0.8713 0.2634 3.31 0.001
GMAT 0.0022825 0.0002649 8.62 0.000
UGPA 0.29731 0.04300 6.91 0.000
Age 0.005435 0.008088 0.67 0.502
S = 0.212057 R-Sq = 56.7% R-Sq(adj) = 56.1%
Analysis of Variance
Source DF SS MS F P
Regression 3 11.6761 3.8920 86.55 0.000
Residual Error 198 8.9037 0.0450
Total 201 20.5798

7. 7
Source DF Seq SS
GMAT 1 9.3921
UGPA 1 2.2637
Age 1 0.0203
Unusual Observations
Obs GMAT MBA GPA Fit SE Fit Residual St Resid
3 510 3.7450 3.2794 0.0470 0.4656 2.25R
20 690 3.8420 3.3344 0.0412 0.5076 2.44R
34 430 2.8120 2.7542 0.0649 0.0578 0.29 X
39 680 2.9430 3.4696 0.0295 -0.5266 -2.51R
48 650 3.6350 3.1927 0.0408 0.4423 2.13R
70 460 2.7150 2.8183 0.0723 -0.1033 -0.52 X
74 500 3.5680 2.9137 0.0659 0.6543 3.25RX
87 670 3.7930 3.2662 0.0399 0.5268 2.53R
107 570 2.5090 3.0064 0.0272 -0.4974 -2.37R
132 400 2.4680 2.9573 0.0655 -0.4893 -2.43RX
140 460 2.7040 3.0374 0.0522 -0.3334 -1.62 X
142 460 3.4660 2.7994 0.0296 0.6666 3.17R
154 670 3.6260 3.6825 0.0692 -0.0565 -0.28 X
170 610 2.8570 3.3139 0.0183 -0.4569 -2.16R
173 630 3.8940 3.1198 0.0384 0.7742 3.71R
176 560 3.6230 3.4618 0.0524 0.1612 0.78 X
196 500 3.6400 3.2205 0.0462 0.4195 2.03R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
RegressionAnalysis: MBA GPA versus GMAT, UGPA, Age
The regression equation is
MBA GPA = 0.871 + 0.00228 GMAT + 0.297 UGPA + 0.00543 Age
Predictor Coef SE Coef T P
Constant 0.8713 0.2634 3.31 0.001
GMAT 0.0022825 0.0002649 8.62 0.000
UGPA 0.29731 0.04300 6.91 0.000
Age 0.005435 0.008088 0.67 0.502
S = 0.212057 R-Sq = 56.7% R-Sq(adj) = 56.1%

8. 8
Analysis of Variance
Source DF SS MS F P
Regression 3 11.6761 3.8920 86.55 0.000
Residual Error 198 8.9037 0.0450
Total 201 20.5798
Source DF Seq SS
GMAT 1 9.3921
UGPA 1 2.2637
Age 1 0.0203
Unusual Observations
Obs GMAT MBA GPA Fit SE Fit Residual St Resid
3 510 3.7450 3.2794 0.0470 0.4656 2.25R
20 690 3.8420 3.3344 0.0412 0.5076 2.44R
34 430 2.8120 2.7542 0.0649 0.0578 0.29 X
39 680 2.9430 3.4696 0.0295 -0.5266 -2.51R
48 650 3.6350 3.1927 0.0408 0.4423 2.13R
70 460 2.7150 2.8183 0.0723 -0.1033 -0.52 X
74 500 3.5680 2.9137 0.0659 0.6543 3.25RX
87 670 3.7930 3.2662 0.0399 0.5268 2.53R
107 570 2.5090 3.0064 0.0272 -0.4974 -2.37R
132 400 2.4680 2.9573 0.0655 -0.4893 -2.43RX
140 460 2.7040 3.0374 0.0522 -0.3334 -1.62 X
142 460 3.4660 2.7994 0.0296 0.6666 3.17R
154 670 3.6260 3.6825 0.0692 -0.0565 -0.28 X
170 610 2.8570 3.3139 0.0183 -0.4569 -2.16R
173 630 3.8940 3.1198 0.0384 0.7742 3.71R
176 560 3.6230 3.4618 0.0524 0.1612 0.78 X
196 500 3.6400 3.2205 0.0462 0.4195 2.03R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
Residual Plots for MBA GPA

9. 9
Residual
Percent
0.80.40.0-0.4-0.8
99.9
99
90
50
10
1
0.1
Fitted Value
Residual
4.03.53.02.5
0.6
0.3
0.0
-0.3
-0.6
Residual
Frequency
0.80.60.40.20.0-0.2-0.4
40
30
20
10
0
Observation Order
Residual
200180160140120100806040201
0.6
0.3
0.0
-0.3
-0.6
Normal Probability Plot of the Residuals Residuals Versus the Fitted Values
Histogram of the Residuals Residuals Versus the Order of the Data
Residual Plots for MBA GPA
The R-Squared for this model was 56.7, which means that there is quite a good positive
correlation between MBA GPA and GMAT, Undergraduate GPA and Age.
The Hypothesis test
Alpha is 0.05%
H: O, B1 = B2 = B3 = 0
H1: At least one of these is non-Zero
1) B1 P < alpha ( P = 0, alpha = 0.05) Therefore reject null hypothesis. Gmat is
a good predictor of MBA GPA
2) B2 P< alpha (P = 0, alpha = 0.05). Therefore reject null hypothesis.
Undergraduate GPA is a good predictor of MBA GPA
3) B3 P> alpha (P = 0.502, alpha=0.05). Therefore accept null hypothesis. Age
is not a good indicator of MBA GPA.
The F statistic is very high. MSE is much less than MSR. Therefore this is a good model.
The one caveat is that Age is not a good indicator. This could be rejected from the model
to create a better regression analysis according to Ockham’s principle; you should have
as few variables as possible to predict the relationship between variables and MBA GPA.
My conclusion is that MBA GPA can be predicted to a large extent through
Undergraduate GPA and GMAT scores.

10. 10
MBA GPA
AGE
4.003.753.503.253.002.752.50
34
32
30
28
26
24
22
Scatterplot of AGE vs MBA GPA

11. 11
UGPA
MBAGPA
4.03.53.02.52.0
4.00
3.75
3.50
3.25
3.00
2.75
2.50
MBA GPA V UG GPA
Residual
Percent
1.00.50.0-0.5-1.0
99.9
99
90
50
10
1
0.1
Fitted Value
Residual
3.63.43.23.02.8
1.0
0.5
0.0
-0.5
-1.0
Residual
Frequency
0.90.60.30.0-0.3-0.6-0.9
40
30
20
10
0
Observation Order
Residual
200180160140120100806040201
1.0
0.5
0.0
-0.5
-1.0
Normal Probability Plot of the Residuals Residuals Versus the Fitted Values
Histogram of the Residuals Residuals Versus the Order of the Data
Residual Plots for MBA GPA

12. 12
RegressionAnalysis: MBA GPA versus UGPA
Weighted analysis using weights in MBA GPA
The regression equation is
MBA GPA = 1.78 + 0.485 UGPA
Predictor Coef SE Coef T P
Constant 1.7815 0.1277 13.96 0.000
UGPA 0.48509 0.04297 11.29 0.000
S = 0.449942 R-Sq = 38.9% R-Sq(adj) = 38.6%
PRESS = 40.7521 R-Sq(pred) = 38.53%
Analysis of Variance
Source DF SS MS F P
Regression 1 25.805 25.805 127.47 0.000
Residual Error 200 40.490 0.202
Total 201 66.295
Unusual Observations
Obs UGPA MBA GPA Fit SE Fit Residual St Resid
12 3.96 3.8360 3.7049 0.0474 0.1311 0.58 X
20 2.59 3.8420 3.0355 0.0235 0.8065 3.53R
25 2.94 3.6970 3.2072 0.0178 0.4898 2.10R
44 3.96 3.6610 3.7044 0.0474 -0.0434 -0.19 X
48 2.38 3.6350 2.9355 0.0300 0.6995 2.99R
57 2.92 2.5850 3.1999 0.0178 -0.6149 -2.20R
74 2.45 3.5680 2.9680 0.0277 0.6000 2.54R
85 2.83 3.6820 3.1538 0.0184 0.5282 2.26R
87 2.49 3.7930 2.9899 0.0263 0.8031 3.50R
127 3.76 3.9520 3.6074 0.0395 0.3446 1.55 X
132 3.40 2.4680 3.4294 0.0264 -0.9614 -3.37R
137 3.77 3.8800 3.6122 0.0399 0.2678 1.19 X
140 3.35 2.7040 3.4075 0.0250 -0.7035 -2.58R
155 3.91 4.0000 3.6768 0.0451 0.3232 1.47 X
173 2.32 3.8940 2.9089 0.0320 0.9851 4.36R
176 3.90 3.6230 3.6743 0.0449 -0.0513 -0.22 X

13. 13
200 4.00 3.7200 3.7219 0.0488 -0.0019 -0.01 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
* WARNING * the prediction interval output assumes a weight of 1. An
Adjustment must be made if a weight other than 1 is used.
Predicted Values for New Observations
Residual
Percent
0.80.40.0-0.4-0.8
99.9
99
90
50
10
1
0.1
Fitted Value
Residual
4.03.53.02.5
0.6
0.3
0.0
-0.3
-0.6
Residual
Frequency
0.80.60.40.20.0-0.2-0.4
48
36
24
12
0
Observation Order
Residual
200180160140120100806040201
0.6
0.3
0.0
-0.3
-0.6
Normal Probability Plot of the Residuals Residuals Versus the Fitted Values
Histogram of the Residuals Residuals Versus the Order of the Data
Residual Plots for MBAGPA
RegressionAnalysis: MBAGPA versus GMAT, UGPA
The regression equation is
MBAGPA = 1.02 + 0.00222 GMAT + 0.302 UGPA
Predictor Coef SE Coef T P
Constant 1.0234 0.1346 7.60 0.000
GMAT 0.0022226 0.0002491 8.92 0.000
UGPA 0.30163 0.04245 7.10 0.000
S = 0.211764 R-Sq = 56.6% R-Sq(adj) = 56.2%

14. 14
Analysis of Variance
Source DF SS MS F P
Regression 2 11.6558 5.8279 129.96 0.000
Residual Error 199 8.9240 0.0448
Total 201 20.5798
Source DF Seq SS
GMAT 1 9.3921
UGPA 1 2.2637
Unusual Observations
Obs GMAT MBAGPA Fit SE Fit Residual St Resid
3 510 3.7450 3.2811 0.0469 0.4639 2.25RX
20 690 3.8420 3.3367 0.0410 0.5053 2.43R
39 680 2.9430 3.4638 0.0282 -0.5208 -2.48R
48 650 3.6350 3.1857 0.0394 0.4493 2.16R
57 500 2.5850 3.0167 0.0236 -0.4317 -2.05R
74 500 3.5680 2.8725 0.0242 0.6955 3.31R
87 670 3.7930 3.2639 0.0397 0.5291 2.54R
95 520 3.5170 3.3097 0.0460 0.2073 1.00 X
107 570 2.5090 3.0097 0.0267 -0.5007 -2.38R
132 400 2.4680 2.9371 0.0581 -0.4691 -2.30RX
137 760 3.8800 3.8510 0.0448 0.0290 0.14 X
142 460 3.4660 2.8044 0.0287 0.6616 3.15R
155 760 4.0000 3.8911 0.0468 0.1089 0.53 X
170 610 2.8570 3.3179 0.0173 -0.4609 -2.18R
173 630 3.8940 3.1247 0.0376 0.7693 3.69R
176 560 3.6230 3.4451 0.0460 0.1779 0.86 X
196 500 3.6400 3.2278 0.0448 0.4122 1.99 X
Therefore 56.6% of the MBA GPA is determined by GMAT score and undergraduate
GPA. However it would be interesting to see how this correlation works with data such as
Undergraduate institution. For example, if you could determine a correlation between
MBA GPA, GMAT, UG GPA and institution and major, then you could perhaps be in a
strong position to determine with around 70% accuracy what the MBA GPA of a
potential student is.
Clearly this information is extremely valuable to business schools, since GPA scores is a
major factor in determining the employability of its students. This is especially the case
with fields such as finance and consultancy, where less than a 3.5 GPA is rarely looked

15. 15
at. Therefore I decided to take a look at Undergraduate schools to determine some
correlation. I did not want to include race or sex as a defining factor in my report for
ethical reasons.
MBA GPA V SCHOOL
Unfortunately there doesn’t seem to be a large correlation between schools and MBA GPA, only
around 12%
RegressionAnalysis: MBA GPA versus School
The regression equation is
MBA GPA = 2.78 + 0.113 School
Predictor Coef SE Coef T P
Constant 2.78497 0.07521 37.03 0.000
School 0.11254 0.02075 5.42 0.000
S = 0.299501 R-Sq = 12.8% R-Sq(adj) = 12.4%
Residual Plots for MBA GPA

16. 16
School
MBAGPA
54321
4.00
3.75
3.50
3.25
3.00
2.75
2.50
Scatterplot of MBA GPA vs School
I thought it would be interesting to see if there was a better correlation between
undergraduate major and MBA GPA. Generally, students who have studies subjects such
as engineering seem to get higher scores. However this may just be anecdotal evidence.
There is only about a 2% correlation for MBA GPA and major, so it appears that this
evidence is mainly anecdotal. However I would like to experiment more on this with my
own data on methods. For I am relying on the data passed to me. I would ideally like to
run some kind of comparison between liberal arts majors/ political science/ Business and
finally engineering/ pure science to get a better picture of the correlations.
RegressionAnalysis: MBA GPA versus Major
The regression equation is
MBA GPA = 3.07 + 0.0604 Major
Predictor Coef SE Coef T P
Constant 3.06868 0.05129 59.83 0.000
Major 0.06040 0.02585 2.34 0.020
S = 0.316490 R-Sq = 2.7% R-Sq(adj) = 2.2%

17. 17
Major
MBAGPA
3.02.52.01.51.0
4.00
3.75
3.50
3.25
3.00
2.75
2.50
Scatterplot of MBA GPA vs Major
RegressionAnalysis: MBA GPA versus Age
The regression equation is
MBA GPA = 3.68 - 0.0212 Age
Predictor Coef SE Coef T P
Constant 3.6849 0.2748 13.41 0.000
Age -0.02119 0.01142 -1.86 0.065
S = 0.318053 R-Sq = 1.7% R-Sq(adj) = 1.2%
PRESS = 20.7420 R-Sq(pred) = 0.00%
Analysis of Variance
Source DF SS MS F P
Regression 1 0.3483 0.3483 3.44 0.065
Residual Error 200 20.2315 0.1012
Total 201 20.5798

18. 18
As you can see from the diagram, the order of correlation of data is in descending order,
from MBA to GMAT of 46%, through to MBA to age of 1.7% R-Squared.
Conclusion
Therefore I would conclude that the best indication of MBA GPA is undergraduate GPA
and GMAT. However people at lowest and highest range of GMAT should probably be
looked at more carefully, since other factors seemed to play a much larger part, for these
parameters. I would also recommend going into far more detail on schools and
undergraduate degree. Perhaps some kind of personality profiling would be useful in
order to determine sociability/ extroversion and interpersonal skills that could be
factored into the model to achieve an ideal correlation of around 70 % accuracy.
Importance of Variables
0
10
20
30
40
50
GMAT UGPA School Major Age
Variable
Correlation(%)
GMAT
UGPA
School
Major
Age

19. 19
Correlation between MBA GPA and GMAT/ Undergraduate GPA
Residual
Percent
0.750.500.250.00-0.25-0.50
99.9
99
95
90
80
70
60
50
40
30
20
10
5
1
0.1
Normal Probability Plot of the Residuals
(response is MBA GPA)